# Math Help - another normal distribution

1. ## another normal distribution

X is a random variable following a normal distribution. Given the standard deviation is 12, and Pr(X < 25) = .15, find the mean.

Hmm, any help?

2. Originally Posted by scorpion007
X is a random variable following a normal distribution. Given the standard deviation is 12, and Pr(X < 25) = .15, find the mean.

Hmm, any help?
Consider Z=(X-mean(X))/12, then Z~N(0,1)

So if:

Pr(Z<A)=0.15

we may look up the value of A which gives this probability. Doing this
we find A=-1.03643, so the X=25 corresponds to A=-1.03643 or:

-1.03643 = (25-mean(X))/12

so:

mean(X)= 25 + 12*1.03643~=37.44

RonL

3. thanks very much